Fraction Operations: Understanding 4/15 × 30 1/3
Fractions are an essential part of mathematics, and performing operations on them is crucial for solving various problems. In this article, we will explore the concept of multiplying fractions and mixed numbers, using the example of 4/15 × 30 1/3.
Understanding the Multiplication of Fractions
Before we dive into the problem, let's review the basics of fraction multiplication. When multiplying two fractions, we need to follow these steps:
- Multiply the numerators (numbers on top) together
- Multiply the denominators (numbers on the bottom) together
- Write the product as a new fraction
For example, if we want to multiply 1/2 and 3/4, we would do:
- Multiply numerators: 1 × 3 = 3
- Multiply denominators: 2 × 4 = 8
- Write the product: 3/8
Converting Mixed Numbers to Improper Fractions
Before we can multiply 4/15 by 30 1/3, we need to convert the mixed number 30 1/3 to an improper fraction. To do this, we multiply the whole number part (30) by the denominator (3) and then add the numerator (1):
- 30 × 3 = 90
- 90 + 1 = 91
- So, 30 1/3 = 91/3
Now we can rewrite the problem as:
4/15 × 91/3
Multiplying the Fractions
Now that we have two improper fractions, we can multiply them together:
- Multiply numerators: 4 × 91 = 364
- Multiply denominators: 15 × 3 = 45
- Write the product: 364/45
Simplifying the Fraction (Optional)
The resulting fraction 364/45 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 364 and 45 is 1, so the fraction is already in its simplest form.
Conclusion
In conclusion, the result of multiplying 4/15 by 30 1/3 is 364/45. By following the steps outlined above, we can perform fraction multiplication and mixed number conversion with ease. Remember to simplify your fractions whenever possible to make them easier to work with.
